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Finite differences and collocation methods for the solution of the two-dimensional heat equation

✍ Scribed by Jules Kouatchou

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 101 KB
Volume: 17
Category: Article
ISSN: 0749-159X
DOI: 10.1002/1098-2426(200101)17:1<54::aid-num4>3.0.co;2-a

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✦ Synopsis

In this article, we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two-dimensional heat equation. We employ, respectively, second-order and fourth-order schemes for the spatial derivatives, and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is nonsingular. Numerical experiments carried out on serial computers show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

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